Question

A resistor of resistance R is connected to an ideal battery (battery with zero internal resistance). If the value of R is increased, the heat developed in the resistor for equal interval of time will ___.

• A. increase
• B. decrease
• C. remains unchanged
• D. Data insufficient

Answer 1

The correct option is B decrease

Let’s go through this!
Heat dissipated $H=i^{2}Rt$ where the symbols have their usual meanings. Now if the resistance increases, the heat dissipated must increase. Right? Well! NO! That’s not right...
Why?
Here a battery is put across the resistor which maintains a constant potential difference across the resistor. On increasing resistance current (i) will decrease !!!! So the equation H = i^2 Rt is not the right equation to judge the variation (as other variable current also has dependency on resistance)
Let’s write this equation in other form
we know V= iR
so $H=i^{2}Rt=\frac{v^{2}t}{R}$
In this equation V and t are constants, and H, thus varies only with R.
See here, as R increases H decreases…